Simplifying Expressions (Collecting Like Terms) - Examples, Exercises and Solutions

Let's simplify the expression $3x + 4x + 7 + 2$ step-by-step:

• Step 1: Combine Like Terms Involving $x$
  The terms $3x$ and $4x$ are like terms because both involve the variable $x$. To combine them, add their coefficients:
  $3x + 4x = (3 + 4)x = 7x$

• Step 2: Combine Constant Terms
  The expression includes constant terms $7$ and $2$. These can be added together to simplify:
  $7 + 2 = 9$

• Step 3: Write the Simplified Expression
  Now, combine the results from Step 1 and Step 2 to form the final simplified expression:
  $7x + 9$

Therefore, the simplified expression is $7x + 9$.

Reviewing the choices provided, the correct choice is:

• Choice 2: $7x + 9$

This matches our simplified expression, confirming our solution is correct.

To determine if the expressions $18x$ and $2 + 9x$ are equivalent, we'll analyze their structures.

• $18x$ is a linear expression with a single term involving the variable $x$, and its coefficient is 18.
• $2 + 9x$ consists of two terms: a constant term $2$ and a linear term $9x$ with coefficient 9.

For two expressions to be equivalent, each corresponding term must be equal. Here, the expression $18x$ has no constant term, whereas $2 + 9x$ has a constant term of 2. Furthermore, the linear term coefficients differ: $18 \neq 9$.

Therefore, the expressions $18x$ and $2 + 9x$ are not the same. They structurally differ and cannot be made equivalent just through similar values of $x$.

Therefore, the solution to this problem is: No.

To simplify the expression $5 + 0 + 8x - 5$, follow these steps:

• Step 1: Identify and group like terms. In this case, there are constants (5, 0, -5) and a term with a variable (8x).
• Step 2: Combine the constants: $5 + 0 - 5$.
• Step 3: Calculate: $5 - 5 = 0$.

Now, our expression simplifies to $0 + 8x$, which is simply $8x$.

Therefore, the simplified expression is $8x$.

To solve this algebraic problem, follow these steps:

• Step 1: Identify the coefficients of the variable $x$ in the expression $x + x$. Here, the coefficient for each $x$ is 1.
• Step 2: Add the coefficients together. This gives $1 + 1 = 2$.
• Step 3: Multiply the result by the variable. This results in $2x$.

Since the problem is a multiple-choice question, review the available choices to select the correct answer. The expression simplifies to $2x$, which corresponds to choice 3: $2x$.

Therefore, the solution to the problem is $2x$.

To solve this problem, we'll analyze the expressions $3+3+3+3$ and $3 \times 4$ to determine if they are equivalent.

First, evaluate the expression $3+3+3+3$:

• Add the numbers: $3 + 3 = 6$
• Add again: $6 + 3 = 9$
• Add the last $3$: $9 + 3 = 12$

The result of $3+3+3+3$ is $12$.

Next, evaluate the expression $3 \times 4$:

• Perform the multiplication: $3 \times 4 = 12$

The result of $3 \times 4$ is also $12$.

Since both expressions result in the same number, we conclude that

The expressions are the same.

Therefore, the correct answer is Yes.